2013/11/19 by Doleželová, Jana
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1311.4734
This article investigates the relation between the distributional chaos and the existence of a scrambled triple. We show that for a continuous mapping f acting on a compact metric space (X,d), the possession of an infinite extremal distributionally scrambled set is not sufficient for the existence of a scrambled triple. We also construct an invariant Mycielski set with an uncountable extremal distributionally scrambled set without any scrambled triple.